Come join us in the Shifting Seas and Transitive Isles of Living 4th Edition, amazing adventures and great fun guaranteed!
Then to play community 4e in Eberron join us in LEB too! Give life to your characters and contribute to the living settings!

Check out the tutorials at RPTools - Home. There's a pretty neat arena map background I used with maptool in the Ata vs. nerdytenor monster mash game, though it's a bit bigger than most fights will need. But that's not a bad thing.

Anyway, that's how I'd go about the arena mapping if I were doing it right now.

1 - Using Excel, either
A - paste a map in there and line up the grid with the Excel grid (I did this for Necromancer's Skull stealing a map from WotC's archives), or;
B - create a map in Excel itself via colored squares/borders (I'm using this now in Ebon Mirror).

2 - Use icons such as monster images or user profile pics to track combatant locations. You can draw squares of different colors to use as pic borders to differentiate different creatures of the same type pretty easy.

3 - Screen cap it, crop the screen cap in Paint, save as a jpg, upload that to TinyPic.com, and you're golden.

I also paste monster stat blocks into the Excel file for reference, and keep track of round by round actions off to the side in a tracking grid. It's my one-file-fight-friend!

Yes, I think we'd treat it like an adventure, so send the judges an email with a proposal.

Another question is whether you'd allow another DM to step in and run a couple fights if they wanted to?

I'd think it'd be like the Long Arm of Lauto, where just because covaithe DMed the first one, doesn't stop other DMs from coming in and doing others. Given their stand-alone episodic nature, such themed adventure series are perfect for multiple DMs to take turns running.

I may do a Long Arm of Lauto myself after finishing up Ebon Mirror, just to get a little DM work in without having to come up with a long series of encounters or an original plot.

Other idea: I dumped some info on Daunton's underground fighting circuit into the wiki earlier. Its run by Gouki, a big ol' badass from the Kingdom of Jade. His fights are to the death, although that can always be retconned.